I don't think either of the glitches are Time-Turners. Time-Turners have (presumably) been used regularly in Hogwarts since the twins arrived, and it's made clear that these glitches are new:

The Map was an extraordinarily powerful artifact, capable of tracking every sentient being on the school grounds, in real time, by name. Almost certainly, it had been created during the original raising of Hogwarts. It was not good that errors were starting to pop up.